Automorphisms of Hyperbolic Groups and Graphs of Groups
Automorphisms of Hyperbolic Groups and Graphs of Groups
复制标题
双曲群的自同构和群图
DOI：
--
复制
发表时间：
2002
期刊：
影响因子：
--
通讯作者：
G. Levitt
中科院分区：
文献类型：
--
作者：
G. Levitt
使用规范的 JSJ 分裂，我们描述了单端词双曲群 G 的外自同构群 Out(G)。特别地，我们讨论了 Out(G) 在多大程度上实际上是映射类群和自由交换群的直积，并且我们确定了哪些群 Out(G) 是无限的。我们还证明，对于 G 来说，任意无挠双曲群，Out(G) 中只有有限多个挠距元素的共轭类。更一般地，令 Γ 为任意群 G 的群分解的有限图，使得边群 Ge 是刚性的（即 Out(Ge) 是有限的）。我们通过将其与适当定义的顶点组映射类组的直接乘积进行比较来描述 G 保留 Γ 的自同构群。
Using the canonical JSJ splitting, we describe the outer automorphism group Out(G) of a one-ended word hyperbolic group G. In particular, we discuss to what extent Out(G) is virtually a direct product of mapping class groups and a free abelian group, and we determine for which groups Out(G) is infinite. We also show that there are only finitely many conjugacy classes of torsion elements in Out(G), for G any torsion-free hyperbolic group. More generally, let Γ be a finite graph of groups decomposition of an arbitrary group G such that edge groups Ge are rigid (i.e. Out(Ge) is finite). We describe the group of automorphisms of G preserving Γ, by comparing it to direct products of suitably defined mapping class groups of vertex groups.